Technically yes but also no. The recoil from a gun obviously produces force in a certain direction. So obviously if you were to jump and shoot down, this force would be added to your momentum. However in practice no shotgun is strong enough to produce a noticeable effect, like actually capable of moving you higher. Why? Because the same shotgun under normal use would knock you down when you shot it, since it’s capable of pushing your entire weight. It would also probably break your shoulder.
Obligatory don’t try this at home.
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